I don't see the hijab (which I think is the headscarf, rather than the veil covering the face) as a form of oppression. I think it's because I used to work with some Muslim women who sometimes wore them, but not always, so it came across as a personal choice. I see the veil (niqab?) as oppressive though, as I see it as "dehumanising" - by covering the face so much facial expressions are hidden, so it's harder to relate to the women who wear them.

With regards to the picture, the first thing that came to mind is, are the women choosing to dress that way? The woman in the bikini has chosen to wear something that presumably makes her feel good about herself - if she felt that she was getting too much attention from men (or if she started to feel a bit cold), she could choose to wear something less revealing. Does the woman in the niqab have the freedom to take off the veil if she feels uncomfortable? What would be the reaction of her male relatives?

As for whether Americans live in a patriarchal society, I can't really comment (being on the other side of the Atlantic ) However, I think that certainly in Britain we are still male-dominated overall - we have been for centuries, and it will take time for things to change.